201432: [AtCoder]ARC143 C - Piles of Pebbles

Problem Statement

There are $N$ piles of pebbles. Initially, the $i$-th pile has $A_i$ pebbles.

Takahashi and Aoki will play a game using these piles. They will alternately perform the following operation, with Takahashi going first, and the one who becomes unable to do so loses the game.

• Choose one or more piles, and remove the following number of pebbles from each chosen pile: $X$ pebbles if this operation is performed by Takahashi, and $Y$ pebbles if performed by Aoki. Here, a pile with an insufficient number of pebbles cannot be chosen.

Determine the winner of the game if both players play optimally.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq X, Y \leq 10^9$
• $1 \leq A_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$ $X$ $Y$
$A_1$ $A_2$ $\cdots$ $A_N$

Output

If it is Takahashi who will win the game, print First; if it is Aoki, print Second.

Sample Input 1

2 1 1
3 3

Sample Output 1

First

Here is one possible progression of the game.

• Takahashi removes $1$ pebble from both piles.
• Aoki removes $1$ pebble from the $1$-st pile.
• Takahashi removes $1$ pebble from the $1$-st pile.
• Aoki removes $1$ pebble from the $2$-nd pile.
• Takahashi removes $1$ pebble from the $2$-nd pile.

No matter how Aoki plays, Takahashi can always win, so the answer is First.

Sample Input 2

2 1 2
3 3

Sample Output 2

Second